Half-Circle Patterns

Drag any 4x4 image to overlay it on any other.
A variety of interesting patterns results.

The images are a few of the many Latin squares that
can be formed using half-circles as entries. They are the
original form of the images in the diamond theorem that use
not half-circles, but triangular half-squares, as array entries.

© 2009 Steven H. Cullinane

Update of March 15, 2010--

The above patterns were suggested by an artwork from
the Albright-Knox museum shop I received as a gift
in 1975. This was a square box with 16 rotatable spheres,
each half black and half white, embedded in the box's top.

The artwork may have been based on the work of
Paul Talman. A reconstruction, below, indicates
how this may have been done by picturing a detail
of Talman's Kugelbild, a kinetic sculpture
that he probably did around 1968.